arXiv subjects

Ying Xie

Publications and source records attributed to Ying Xie.

At least 19 recordsLinked to original sources

arXiv2026

Recursive Reasoning Exploration: Mathematical Research through Evolving Reasoning Graphs : case study: An Exact Certificate-Degree Theorem for Two-Term Tensor Decompositions : Phase III of the Math Instruments Program

Large collections of manuscripts and research notes offer ways to reuse arguments, while making it harder to retain hypotheses, check claims, and understand how results were obtained. We propose Recursive Reasoning Exploration (RRE), a framework for cumulative mathematical research through evolving reasoning graphs. RRE links claims and jointly required premises to research targets, attempted arguments, counterexamples, checks, and revisions. Each investigation can generate further targets, and its supported outcomes become available to subsequent investigations. This is Phase III of the Math Instruments program: identifying mathematical instruments, reconstructing reusable reasoning, and organizing recursive research from that reasoning. The framework supports human-directed, collaborative, and goal-directed autonomous exploration, with open-ended exploration as a further mode. Its records also provide material for learning how mathematical investigations develop. A complexity research case study establishes an exact theorem: for every complex tensor of order n >= 2 and rank greater than two, the minimum Nullstellensatz certificate degree for its original two-term decomposition equations is 3n. This includes an infinite family whose every flattening has rank at most two. The exploration develops an explicit boundary certificate, a balanced transfer lemma, and an exhaustive argument using classical rank-two geometry. A parallel branch gives bounds 3m + 3 <= delta_m(I_m, N) <= 3m + 6 for every nonzero nilpotent m by m matrix. Six graph revisions record the progression from inherited results to these theorems, with exact arithmetic checks and a replayable exploration history. We present the RRE representation and protocol, the mathematical proofs, visualizations of graph evolution, and a research agenda for shared human-AI exploration, cumulative reuse, and education.

cs.AI↗

arXiv2026

Can System-1-Style Decision Models Replace Dedicated Rerankers in RAG? A Systems Evaluation

Retrieval-augmented generation (RAG) systems often use a dedicated reranker to choose which retrieved candidates reach the language model. Reranking improves relevance but adds latency, so teams look for faster alternatives. System-1style decision models make direct, structured predictions instead of generating long responses. Could one provide comparable reranking quality with less inference overhead? We first screen 21 open-weight models on 11 benchmarks, then compare a promising decision model with a dedicated reranker on identical candidate lists. The default decision-model setup fails on many long candidate sets, so scoring only the requests it completes gives a misleading ranking. Limiting candidate text length largely restores reliability and makes some configurations competitive. A frozen evaluation on new retrieval data supports the reliability and ranking results, but confirms the latency requirement for only one of the two selected configurations. Across workloads, which model ranks better changes, and a tuned reranker remains faster and uses far less GPU memory. A decision model can perform competitive reranking, but replacing a reranker requires weighing quality, latency and memory together, and teams should tune the reranker they already run first.

cs.LG↗

arXiv2026

What the Machine Invented: Mining New Mathematical Instruments from OpenAI's October 2026 Release of AI-Generated Mathematics

On 6 October 2026 OpenAI published an initial 722 AI-written mathematical manuscripts, organized into 372 problem families, in the public repository github.com/openai/math. The release includes claimed solutions to many prominent open problems. We approach this collection as a treasure mine of mathematical ideas. Our aim is to extract new lemmas, constructions, inequalities and proof mechanisms introduced in the source arguments, and to distinguish them from established tools and new combinations of those tools. We call these mathematical instruments. Extraction comes first; their validity, novelty and possible reuse then become subjects for further study. The resulting descriptions also help readers understand the selected papers without having to reconstruct every argument at the outset. We examine 38 families in two groups of 17 and 21, spanning number theory, geometry, analysis, combinatorics, complexity, algebra, operator algebras, topology and mathematical physics. Each entry records the claim, extracted instruments, antecedents and caveats. Eleven cross-cutting patterns connect the entries, and a scoreboard records formalization status and dependencies. Novelty assessments are provisional and sometimes mixed. Selected source comparisons correct mathematical statements, hypotheses and counts; they do not independently establish priority or certify the underlying proofs. No Lean development was compiled or kernel-checked for this survey. We also briefly describe a subsequent application of the signed restriction lemma from family 112 to circuit lower bounds at every fixed depth.

math.HO↗

arXiv2026

Sharp FRS and singularity thresholds for off-diagonal Gram maps

The off-diagonal Gram map for h vectors in an M-dimensional quadratic space is flat with reduced fibers of rational singularities (FRS) in characteristic zero if and only if M > max_{2 <= r <= h} (2h - r + 1 - 2h/r). Equivalently, this gives the exact FRS convolution threshold of x |-> (x_i x_j){i < j}. For its zero-fiber ideal I{M,h}, we also prove lct(I_{M,h}) = min{ binom(h,2), min_{0 <= k <= h-2} ( binom(k+1,2) + M(h-k)/2 ) }. In the strict range, all truncated coefficient maps have geometrically integral complete-intersection fibers and are faithfully flat over Z[1/2], uniformly over graphs on h vertices. The proof uses a sharp weighted estimate for hollow symmetric matrices over finite local principal ideal rings, paired with isotropic lower bounds. Within the established point-counting approach to rational singularities, this estimate also gives an explicit modulus of continuity for Gram-map densities over every local field of odd residue characteristic.

math.AG↗

arXiv2026

Symmetric-determinant apolarity in odd characteristic

Let D_N be the determinant of the generic symmetric N x N matrix, and let differential operators act by ordinary differentiation over a field of odd characteristic p. We determine the apolar ideal of D_N in every size. In addition to the classical quadratic relations, it is generated by one (p-1) x (p-1) determinant of differential variables for each set of 2p-2 indices. These additional generators are minimal modulo the quadratic ideal. An exterior-algebra realization identifies the remaining apolar relations with radicals of invariant pairings for SL_2. Semisimplification gives a Hilbert series in terms of Dyck paths of height at most p-2, and the Steinberg symmetrizer gives the explicit generators of the entire radical. We also compute the ranks of powers of a general linear form. The weak Lefschetz property holds exactly when N <= 2p-2, and the strong Lefschetz property holds exactly when N < p.

math.AC↗

arXiv2026

Derivative and multiplicity loci of elementary symmetric polynomials in positive characteristic

We determine the dimensions of all derivative loci and all higher multiplicity loci of an elementary symmetric polynomial over an algebraically closed field of positive characteristic. For the degree-d polynomial in n variables, set Q = p^{v_p(n-d+1)}. The common zero locus of its order-q derivatives has dimension d - q - 1 + 1_{Q>d-q}, whereas the locus of zeros of multiplicity at least s has dimension d - s + 1_{Q>d}. The order-two case settles the dimension question in a conjecture of Orzel, with a necessary correction when d is a power of p. We classify all components attaining the larger dimension and prove that they are generically smooth. Along the coordinate components in the smaller-dimension cases, we determine the local rings and obtain generic multiplicity exactly Q. Finally, we identify the full translation stabilizer scheme and derive a Frobenius normal form. These results distinguish dimension jumps from infinitesimal thickening and give a uniform description of their dependence on the characteristic.

math.AG↗

arXiv2026

Dimensions of permanental varieties in arbitrary size

Let $I_h(a,b)$ be the ideal generated by the $h\times h$ permanents of a generic $a\times b$ matrix over a field of characteristic different from two. We prove that $\dim K[X]/I_h(a,b)=\max(a,b)(h-1)$ whenever $1\le h\le\min(a,b)$ and $h<\max(a,b)$. Consequently, the critical locus of the permanent of order $n$ has codimension $2n$ for every $n\ge 2$. We also prove that the maximal permanents of a generic $k\times(k+1)$ matrix generate a geometrically reduced complete intersection. The dimension argument uses a pivot expansion and cubic relations in the border variables. Two successive comparisons with highest-degree equations reduce the relevant fibers to a coordinate-support calculation. Reducedness follows from a separate regular-sequence argument and a dimension estimate excluding components over the exceptional locus.

math.AC↗

arXiv2026

Nullstellensatz degree under Hajós joins and vertex identifications

We study the minimum coefficient degree $N_{k,\F}(G)$ of a Nullstellensatz certificate for Bayer's $k$-coloring equations, where the characteristic of $\F$ does not divide $k$. If $J$ is a \HJ\ join of non-$k$-colorable graphs $G,H$ and $m=\max\{N_{k,\F}(G),N_{k,\F}(H)\}$, then $N_{k,\F}(J)\leq m+k$. When deletion of the selected edge makes each input $k$-colorable, we also have $N_{k,\F}(J)\geq m$; the degree congruence then gives $N_{k,\F}(J)\in\{m,m+k\}$. This partially answers a question of Li, Lowenstein, and Omar. For three-coloring over $\F_2$, we construct an infinite $4$-critical family of exact degree seven, attaining the bound at input degree four. In contrast, every graph constructed from $K_4$ solely by \HJ\ joins has degree $O(\log n)$ and a certificate with polynomially many terms: joins preserve treewidth at most three, and balanced separators yield low-degree certificates. Additional vertex identifications are excluded from this obstruction. We classify all single identifications of the $25$-vertex base graph; exactly $36$ preserve degree seven, producing $24$-vertex $4$-critical graphs of treewidth four. A compressed self-join at adjacent true twins prevents degree loss and gives a repeatable rule adding four vertices per round. The rule does not establish degree amplification or preservation of criticality. Exact witnesses and standalone verification programs accompany the finite results.

math.CO↗

arXiv2026

Cross-Subject EEG Emotion Recognition Based on Temporal Asynchronous Alignment Contrastive Learning

With the advancement of science and technology, the importance of emotion research has become increasingly evident. Electroencephalography (EEG)-based emotion recognition has emerged as an active research area in recent years, owing to its objectivity and high temporal resolution. However, most existing methods focus on optimizing encoder structures to enhance feature extraction capabilities, while paying relatively little attention to similarity calculation strategies, particularly overlooking the potential temporal misalignment of responses among different subjects. To address these shortcomings, this paper draws inspiration from the late interaction mechanism of ColBERT in natural language processing (NLP) and proposes a Temporal Asynchronous Alignment-based Contrastive Learning (TA2CL) framework. This method transforms the traditional global "hard alignment" similarity calculation approach into a fine-grained local matching mechanism, enabling the model to adaptively search for and align "locally highly correlated" segments between two EEG signals, thereby effectively mitigating the effects of inter-subject differences and temporal delays. Experimental results demonstrate that the proposed method achieves strong performance across multiple public datasets. Specifically, on the FACED dataset, it achieves an accuracy of 64.5% for the nine-class classification task and 79.5% for the binary classification task, while on the SEED and SEED-V datasets, it achieves accuracies of 86.4% and 70.1%, respectively, validating the method's effectiveness and generalization capability.

cs.HC↗

arXiv2026

Quantization commutes with reduction for coisotropic A-branes

On a Hamiltonian $G$-manifold $X$, we define the notion of $G$-invariance of coisotropic A-branes $B$. Under neat assumptions, we give a Marsden-Weinstein-Meyer type construction of a coisotropic A-brane $B_{\operatorname{red}}$ on $X // G$ from $B$, recovering the usual construction when $B$ is Lagrangian. For a canonical coisotropic A-brane $B_{\operatorname{cc}}$ on a holomorphic Hamiltonian $G_\mathbb{C}$-manifold $X$, there is a fibration of $(B_{\operatorname{cc}})_{\operatorname{red}}$ over $X // G_\mathbb{C}$. We also show that `intersections of A-branes commute with reduction'. When $X = T^*M$ for $M$ being compact Kähler with a Hamiltonian $G$-action, Guillemin-Sternberg `quantization commutes with reduction' theorem can be interpreted as $\operatorname{Hom}_{X // G}(B_{\operatorname{red}}, (B_{\operatorname{cc}})_{\operatorname{red}}) \cong \operatorname{Hom}_X(B, B_{\operatorname{cc}})^G$ with $B = M$.

math.SG↗

arXiv2026

General365: Benchmarking General Reasoning in Large Language Models Across Diverse and Challenging Tasks

Contemporary large language models (LLMs) have demonstrated remarkable reasoning capabilities, particularly in specialized domains like mathematics and physics. However, their ability to generalize these reasoning skills to more general and broader contexts--often termed general reasoning--remains under-explored. Unlike domain-specific reasoning, general reasoning relies less on expert knowledge but still presents formidable reasoning challenges, such as complex constraints, nested logical branches, and semantic interference. To address this gap, we introduce General365, a benchmark specifically designed to assess general reasoning in LLMs. By restricting background knowledge to a K-12 level, General365 explicitly decouples reasoning from specialized expertise. The benchmark comprises 365 seed problems and 1,095 variant problems across eight categories, ensuring both high difficulty and diversity. Evaluations across 26 leading LLMs reveal that even the top-performing model achieves only 62.8% accuracy, in stark contrast to the near-perfect performances of LLMs in math and physics benchmarks. These results suggest that the reasoning abilities of current LLMs are heavily domain-dependent, leaving significant room for improvement in broader applications. We envision General365 as a catalyst for advancing LLM reasoning beyond domain-specific tasks toward robust, general-purpose real-world scenarios. Code, Dataset, and Leaderboard: https://general365.github.io

cs.CL↗

arXiv2026

Self-Monitoring Benefits from Structural Integration: Lessons from Metacognition in Continuous-Time Multi-Timescale Agents

Self-monitoring capabilities -- metacognition, self-prediction, and subjective duration -- are often proposed as useful additions to reinforcement learning agents. But do they actually help? We investigate this question in a continuous-time multi-timescale agent operating in predator-prey survival environments of varying complexity, including a 2D partially observable variant. We first show that three self-monitoring modules, implemented as auxiliary-loss add-ons to a multi-timescale cortical hierarchy, provide no statistically significant benefit across 20 random seeds, 1D and 2D predator-prey environments with standard and non-stationary variants, and training horizons up to 50,000 steps. Diagnosing the failure, we find the modules collapse to near-constant outputs (confidence std < 0.006, attention allocation std < 0.011) and the subjective duration mechanism shifts the discount factor by less than 0.03%. Policy sensitivity analysis confirms the agent's decisions are unaffected by module outputs in this design. We then show that structurally integrating the module outputs -- using confidence to gate exploration, surprise to trigger workspace broadcasts, and self-model predictions as policy input -- produces a medium-large improvement over the add-on approach (Cohen's d = 0.62, p = 0.06, paired) in a non-stationary environment. Component-wise ablations reveal that the TSM-to-policy pathway contributes most of this gain. However, structural integration does not significantly outperform a baseline with no self-monitoring (d = 0.15, p = 0.67), and a parameter-matched control without modules performs comparably, so the benefit may lie in recovering from the trend-level harm of ignored modules rather than in self-monitoring content. The architectural implication is that self-monitoring should sit on the decision pathway, not beside it.

cs.AI↗

arXiv2026

VibeGuard: A Security Gate Framework for AI-Generated Code

"Vibe coding," in which developers delegate code generation to AI assistants and accept the output with little manual review, has gained rapid adoption in production settings. On March 31, 2026, Anthropic's Claude Code CLI shipped a 59.8 MB source map file in its npm package, exposing roughly 512,000 lines of proprietary TypeScript. The tool had itself been largely vibe-coded, and the leak traced to a misconfigured packaging rule rather than a logic bug. Existing static-analysis and secret-scanning tools did not cover this failure mode, pointing to a gap between the vulnerabilities AI tends to introduce and the vulnerabilities current tooling is built to find. We present VibeGuard, a pre-publish security gate that targets five such blind spots: artifact hygiene, packaging-configuration drift, source-map exposure, hardcoded secrets, and supply-chain risk. In controlled experiments on eight synthetic projects (seven vulnerable, one clean control), VibeGuard achieved 100% recall, 89.47% precision (F1 = 94.44%), and correct pass/fail gate decisions on all eight projects across three policy levels. We discuss how these results inform a defense-in-depth workflow for teams that rely on AI code generation.

cs.CR↗

arXiv2026

Learning to Forget: Sleep-Inspired Memory Consolidation for Resolving Proactive Interference in Large Language Models

Large language models (LLMs) suffer from proactive interference (PI): outdated information in the context window disrupts retrieval of current values. This interference degrades retrieval accuracy log-linearly as stale associations accumulate, a bottleneck that persists regardless of context length and resists prompt-engineering mitigations. Biological brains resolve an analogous challenge through sleep-dependent memory consolidation: synaptic downscaling, selective replay, and targeted forgetting. We propose SleepGate, a biologically inspired framework that augments transformer-based LLMs with a learned sleep cycle over the key-value (KV) cache. SleepGate introduces three mechanisms: (1) a conflict-aware temporal tagger detecting when new entries supersede old ones; (2) a lightweight forgetting gate trained to selectively evict or compress stale cache entries; and (3) a consolidation module that merges surviving entries into compact summaries. These components activate periodically during inference in sleep micro-cycles, governed by an adaptive entropy-based trigger. We formalize a dual-phase training objective jointly optimizing language modeling during the wake phase and post-consolidation retrieval during the sleep phase. Theoretical analysis shows SleepGate reduces the interference horizon from O(n) to O(log n). In experiments with a small-scale transformer (4 layers, 793K parameters), SleepGate achieves 99.5% retrieval accuracy at PI depth 5 and 97.0% at depth 10, while all five baselines -- full KV cache, sliding window, H2O, StreamingLLM, and decay-only ablation -- remain below 18%. Our framework offers an architecture-level solution that prompt engineering cannot address.

cs.AI↗

arXiv2026

Lagrangian Intersections, Symplectic Reduction and Kirwan Surjectivity

Given a smooth holomorphic symplectic variety $X$ with a Hamiltonian $G$-action, $G$-invariant Lagrangians $C's$ induce Lagrangians in the symplectic quotient $X// G$. Given clean intersections $B=C_1\cap C_2$ whose conormal sequence splits, we show that $$C_1/G\times_{X// G} C_2/G\cong T^{\vee}[-1](B/G).$$ When $det(N_{B/C_2})$ is torsion, we have $Ext^{\bullet}_{X// G}(\mathcal{O}_{C_1/G}, \mathcal{O}_{C_2/G})\cong H^{\bullet}_G(B, det(N_{B/C_2})_δ)$ provided that the Hodge-to-de Rham degeneracy holds. Furthermore, we have a generalized version of Kirwan surjectivity $Ext^{\bullet}_{X// G}(\mathcal{O}_{C_1/G}, \mathcal{O}_{C_2/G})\twoheadrightarrow Ext^{\bullet}_{X^{ss}// G}(\mathcal{O}_{C_1^{ss}/G}, \mathcal{O}_{C_2^{ss}/G})$ if $B$ is proper. When $C_1=C_2$, this is the Kirwan surjectivity, which is now interpreted as the symmetry commutes with reduction problem in 3d B-model. We also obtain similar results for $K_{C_1/G}^{1/2}$ and $K_{C_2/G}^{1/2}$.

math.AG↗

arXiv2025

Inferring Latent Market Forces: Evaluating LLM Detection of Gamma Exposure Patterns via Obfuscation Testing

We introduce obfuscation testing, a novel methodology for validating whether large language models detect structural market patterns through causal reasoning rather than temporal association. Testing three dealer hedging constraint patterns (gamma positioning, stock pinning, 0DTE hedging) on 242 trading days (95.6% coverage) of S&P 500 options data, we find LLMs achieve 71.5% detection rate using unbiased prompts that provide only raw gamma exposure values without regime labels or temporal context. The WHO-WHOM-WHAT causal framework forces models to identify the economic actors (dealers), affected parties (directional traders), and structural mechanisms (forced hedging) underlying observed market dynamics. Critically, detection accuracy (91.2%) remains stable even as economic profitability varies quarterly, demonstrating that models identify structural constraints rather than profitable patterns. When prompted with regime labels, detection increases to 100%, but the 71.5% unbiased rate validates genuine pattern recognition. Our findings suggest LLMs possess emergent capabilities for detecting complex financial mechanisms through pure structural reasoning, with implications for systematic strategy development, risk management, and our understanding of how transformer architectures process financial market dynamics.

q-fin.ST↗

arXiv2025

Artificial Intelligence-Enabled Holistic Design of Catalysts Tailored for Semiconducting Carbon Nanotube Growth

Catalyst design is crucial for materials synthesis, especially for complex reaction networks. Strategies like collaborative catalytic systems and multifunctional catalysts are effective but face challenges at the nanoscale. Carbon nanotube synthesis contains complicated nanoscale catalytic reactions, thus achieving high-density, high-quality semiconducting CNTs demands innovative catalyst design. In this work, we present a holistic framework integrating machine learning into traditional catalyst design for semiconducting CNT synthesis. It combines knowledge-based insights with data-driven techniques. Three key components, including open-access electronic structure databases for precise physicochemical descriptors, pre-trained natural language processing-based embedding model for higher-level abstractions, and physical - driven predictive models based on experiment data, are utilized. Through this framework, a new method for selective semiconducting CNT synthesis via catalyst - mediated electron injection, tuned by light during growth, is proposed. 54 candidate catalysts are screened, and three with high potential are identified. High-throughput experiments validate the predictions, with semiconducting selectivity exceeding 91% and the FeTiO3 catalyst reaching 98.6%. This approach not only addresses semiconducting CNT synthesis but also offers a generalizable methodology for global catalyst design and nanomaterials synthesis, advancing materials science in precise control.

cond-mat.mtrl-sci↗

arXiv2025

TWLR: Text-Guided Weakly-Supervised Lesion Localization and Severity Regression for Explainable Diabetic Retinopathy Grading

Accurate medical image analysis can greatly assist clinical diagnosis, but its effectiveness relies on high-quality expert annotations Obtaining pixel-level labels for medical images, particularly fundus images, remains costly and time-consuming. Meanwhile, despite the success of deep learning in medical imaging, the lack of interpretability limits its clinical adoption. To address these challenges, we propose TWLR, a two-stage framework for interpretable diabetic retinopathy (DR) assessment. In the first stage, a vision-language model integrates domain-specific ophthalmological knowledge into text embeddings to jointly perform DR grading and lesion classification, effectively linking semantic medical concepts with visual features. The second stage introduces an iterative severity regression framework based on weakly-supervised semantic segmentation. Lesion saliency maps generated through iterative refinement direct a progressive inpainting mechanism that systematically eliminates pathological features, effectively downgrading disease severity toward healthier fundus appearances. Critically, this severity regression approach achieves dual benefits: accurate lesion localization without pixel-level supervision and providing an interpretable visualization of disease-to-healthy transformations. Experimental results on the FGADR, DDR, and a private dataset demonstrate that TWLR achieves competitive performance in both DR classification and lesion segmentation, offering a more explainable and annotation-efficient solution for automated retinal image analysis.

cs.CV↗